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Renyi Entropy of Progressively Censored Data

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Book cover Ordered Data Analysis, Modeling and Health Research Methods

Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 149))

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Abstract

In this paper, we discuss the calculation of Renyi entropy in a set of consecutive order statistics (OS) and a set of progressively Type-II censored OS . We propose a useful, but indirect, computational approach for computing the Renyi entropy of consecutive order statistics that simplifies the calculations. Some recurrence relations for the Renyi entropy of a set of consecutive order statistics are also derived to facilitate the Renyi entropy computation using the proposed decomposition. Moreover, an extension of the calculation of Renyi entropy for a set of progressively Type-II censored OS is established. Efficient methods are derived which simplify the computation of the Renyi entropy in both settings.

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Acknowledgments

It is a pleasure to contribute to this volume honoring Professor Nagaraja, a prolific researcher in the area of order statistics, record values and health research methods, and we wish him many more years of active academic life. The authors would like to express deep thanks to the referees for their helpful comments and suggestions which led to a considerable improvement in the presentation of this paper. The authors are thankful to Qassim University which provided financial support for this work under Grant SR-D-2819.

Author information

Authors and Affiliations

  1. Department of Mathematics, Faculty of Science, Qassim University, Al-Montazah, 1300, Al Qassim, 51431, Saudi Arabia

    Z. A. Abo-Eleneen

  2. Department of Mathematics, Faculty of Science, Qassim University, 6644, Al Qassim, 51452, Saudi Arabia

    B. Almohaimeed

Authors
  1. Z. A. Abo-Eleneen
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  2. B. Almohaimeed
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Corresponding author

Correspondence to Z. A. Abo-Eleneen .

Editor information

Editors and Affiliations

  1. Department of Mathematical Sciences FO 35, University of Texas at Dallas, Richardson, Texas, USA

    Pankaj Choudhary

  2. Fordham University, New York, New York, USA

    Chaitra H. Nagaraja

  3. Southern Methodist University, Dallas, Texas, USA

    Hon Keung Tony Ng

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Abo-Eleneen, Z.A., Almohaimeed, B. (2015). Renyi Entropy of Progressively Censored Data. In: Choudhary, P., Nagaraja, C., Ng, H. (eds) Ordered Data Analysis, Modeling and Health Research Methods. Springer Proceedings in Mathematics & Statistics, vol 149. Springer, Cham. https://doi.org/10.1007/978-3-319-25433-3_6

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